1. Field of the Invention
The present invention relates to a method for laser cooling of atoms and an apparatus therefore. More specifically, the present invention relates to a coherent light source for laser cooling atoms, and to a method for laser cooling a variety of atoms, such as silicon atoms and germanium atoms, each having a plurality of magnetic sublevels.
2. Description of the Related Art
In recent years, developments in the field of laser cooling of atoms has exhibited quantum leaps, starting with substantiation of Bose-Einstein""s condensation and breakthroughs with atom lasers, nonlinear atom optics and the like.
In the laser cooling field, if it becomes possible to realize laser cooling of semiconductor atoms, such as silicon and germanium, instead of alkaline metal atoms and the like (which have been heretofore an object of laser cooling), novel developments can be expected from an engineering point of view. Hence, expansion in the possibilities of application are inestimable.
In these circumstances, there has been a strong need for provision of a technology for laser-cooling a variety of atoms, including semiconductor atoms, such as silicon and germanium.
The present invention has been made in view of the needs involved in the prior art as described above.
An object of the present invention is to provide a method for laser cooling of atoms by which it becomes possible to laser-cool a variety of atoms, including semiconductor atoms such as silicon and germanium, and an apparatus therefor as well as a coherent light source used in the apparatus.
In order to achieve the above-described objects, a method for laser cooling atoms and an apparatus therefor as well as a coherent light source used for laser cooling atoms are implemented in accordance with a manner as described hereinafter.
Laser cooling of atoms means herein a cooling method wherein the atoms collide against (are scattered with) a laser beam to repeat absorption and spontaneous emission of light, whereby kinetic energy of the atoms is released into such spontaneous emissions of light, whereby the atoms are cooled.
Such a process for laser cooling of atoms can be classified into a stage wherein atoms are sufficiently decelerated, and a stage wherein the atoms decelerated sufficiently are cooled. In such deceleration of atoms and cooling of atoms, a scattering force function occurs, as shown in FIG. 1.
In the following, xe2x80x9cdeceleration of atoms due to scattering forcexe2x80x9d and xe2x80x9ccooling of atoms due to scattering forcexe2x80x9d will be described in detail.
First, cooling of atoms due to a scattering force will be described. The cooling of atoms due to a scattering force relates to so-called xe2x80x9cDoppler coolingxe2x80x9d. Namely, Doppler shift acts most effectively with respect to cooling of atoms, which have been decelerated to around several times wider width than natural width.
In order to effect cooling of atoms by means of spontaneous emission, it is required that an average energy of photons emitted be higher than that of photons absorbed. Namely, Doppler cooling means to realize such a situation wherein an average energy of emitted photons is higher than that of absorbed photons. A particularly effective negative detuning amount is around a natural width (half width at half maximum) of resonance.
Incidentally, since a natural width (half width at half maximum) of silicon is around 28 MHz, a laser having a linewidth of the same degree as, or lower degree than, that of the natural width, i.e., around 28 MHz is required for Doppler cooling. Furthermore, such a laser takes about 130 microseconds until it reaches 220xcexc Kelvin which corresponds to the Doppler cooling temperature. Therefore, it is required to use a continuous wave (CW) light source.
It is to be noted that the natural width (half width at half maximum) of silicon, the Doppler cooling temperature, and the time (stop time) required for reaching 220xcexc Kelvin corresponding to the Doppler cooling temperature are determined by the mathematical expressions shown in FIG. 2.
Next, deceleration of atoms due to a scattering force will be described herein. In this case, a melting point of silicon is 1414xc2x0 C., while a melting point of germanium is 958.5xc2x0 C. The melting points of both of the materials are relatively high melting points, respectively.
A velocity of a silicon atom, which is ran off from the surface by means of electron-beam evaporation, exhibits a Boltzmann distribution centering on about 1000 m/s (meter per second). A half-value width thereof is wide, i.e., about 1500 m/s or more, so that it is about 6 GHz (gigahertz) in a resonance frequency region.
Namely, Doppler broadening (Doppler width) due to velocity broadening is about 6 GHz at melting temperature.
Accordingly, when a frequency of a single frequency coherent light source is changed with a lapse of time to effect chirped cooling in the case where the single frequency coherent light source is used, it becomes possible to decelerate atoms.
On one hand, it may be arranged to use a picosecond laser for decelerating atoms. Namely, in pulses of Fourier transform-limit, 100 picoseconds can involve a frequency zone of 10 GHz. In other words, when the picosecond laser is used, atomic beams, which are in Doppler velocity broadening, can be decelerated at the same time.
Doppler width is determined by the numerical expression shown in FIG. 3.
The reason why laser cooling of silicon atoms is difficult resides not only in that a cooling wavelength is short, but also in that energy level in a ground state, i.e., its cooling lower level being in a ground level involves a plurality of magnetic subsidiary levels, and specifically, three magnetic subsidiary levels.
More specifically, there are three magnetic subsidiary levels as its cooling lower level being a ground level in silicon atom, so that a magnetooptic trap cannot be prepared as in case of alkaline metal atom. This is a major cause of difficulty in laser cooling of silicon atoms.
Referring to FIGS. 4(a) and 4(b), a detailed explanation will be further continued. In silicon atom, a magnetic quantum number m is degenerated in three magnetic subsidiary levels xe2x80x9cm=xe2x88x921xe2x80x9d, xe2x80x9cm=0xe2x80x9d, and xe2x80x9cm=+1xe2x80x9d in energy level in a ground state, i.e., its cooling lower level (3s2p2 3P1, J=1) being the ground level.
In order to laser-cool silicon atoms, it is required that laser beams are emitted to the silicon atoms to excite them, whereby their energy level is elevated from their cooling lower level in their ground state to their cooling upper level (3 s3 p24s3P0, J=0) being their excitation level.
As a result, the silicon atoms are excited by means of emission of laser beams, whereby they are elevated to the cooling upper level. However, such silicon atoms excited from the cooling lower level to the cooling upper level return again to the cooling lower level after expiring spontaneous emission lifetime.
In this case, silicon atoms in the cooling upper level return equivalently to three magnetic subsidiary levels xe2x80x9cm=xe2x88x921xe2x80x9d, xe2x80x9cm=0xe2x80x9d, and xe2x80x9cm=+1xe2x80x9d with one third each of them in the case where the silicon atoms return from the cooling upper level to the cooling lower level (a solution is obtained from the simultaneous differential equations shown in FIG. 4(b).).
On one hand, silicon atoms in the magnetic subsidiary level of xe2x80x9cm=xe2x88x921xe2x80x9d being its cooling lower level in a ground state are excited to its cooling upper level when laser beams of right-handed polarized light ("sgr"+) were emitted to such silicon atoms, silicon atoms in the magnetic subsidiary level of xe2x80x9cm=0xe2x80x9d being its cooling lower level in a ground state are excited to its cooling upper level when laser beams of linearly polarized light (n) were emitted to such silicon atoms, and silicon atoms in the magnetic subsidiary level of xe2x80x9cm=+1xe2x80x9d being its cooling lower level in a ground state are excited to its cooling upper level when laser beams of left-handed polarized light ("sgr"xe2x88x92) were emitted to such silicon atoms.
Accordingly, when it is intended to implement laser cooling of silicon atoms by emitting, for example, linearly polarized light, only the silicon atoms in the magnetic subsidiary level xe2x80x9cm=0xe2x80x9d among cooling lower levels being in a ground state are excited to its cooling upper level. Then, the silicon atoms thus excited to the cooling upper level return to the magnetic subsidiary levels after expiring spontaneous emission lifetime wherein only one third of the silicon atoms return to the magnetic subsidiary level of xe2x80x9cm=0xe2x80x9d among cooling lower levels being in a ground state. Hence, silicon atoms, which are to be excited from their cooling lower level being in their ground state to their cooling upper level, decrease gradually, so that a magneto-optic trap as in a case of alkaline metal atoms could not have been prepared.
Likewise, since there is a plurality of magnetic subsidiary levels in also germanium atom as its cooling lower level, laser cooling of germanium atoms was difficult.
For the sake of overcoming such difficulty as described above, a method for laser cooling of atoms according to the present,invention is arranged such that in case of laser-cooling the atoms each involving a plurality of magnetic subsidiary levels as its cooling lower level, each laser beam having a plurality of polarized light in response to the plurality of magnetic subsidiary levels being its cooling lower level in a ground state is emitted sequentially to the atoms with a predetermined time interval. In other words, the method is to control time-varyingly polarized light in a laser beam by emitting repeatedly such laser beam involving different polarized light in order in each predetermined period of time.
In the case where a laser beam involving different polarized light is emitted repeatedly in order in each predetermined period of time, it is arranged such that photons are struck on an atom successively with a time interval corresponding to twice longer than a spontaneous emission lifetime of the atom, i.e., which is a time required for absorptionxe2x80x94emission of one photon, whereby an atom being in its cooling lower level in a ground state can be excited efficiently to its cooling upper level.
Accordingly, a method for laser cooling atoms each involving a plurality of magnetic subsidiary levels as its cooling lower level being in a ground state in energy level of the present invention comprises emitting sequentially each coherent light of a predetermined wavelength containing a plurality of different polarized light to the atoms in response to the plurality of magnetic subsidiary levels being the cooling lower level in the ground state in an atom, which is an object to be laser-cooled, while keeping a predetermined time interval.
Furthermore, the method for laser cooling of atoms described in the above invention wherein the predetermined time interval is that substantially twice longer than spontaneous emission lifetime of the atom corresponding to a time required for absorptionxe2x80x94emission of one photon.
Moreover, an apparatus for laser cooling of atoms for laser-cooling atoms each involving a plurality of magnetic subsidiary levels as its cooling lower level being in a ground state in energy level according to the present invention comprises a coherent light source for producing a coherent light having a predetermined wavelength; a polarized light control means for controlling polarized light of the coherent light output from the coherent light source to emit the coherent light of different polarized light to the atom with a predetermined time interval; and the polarized light of the coherent light emitted from the polarized light control means corresponds respectively to the plurality of different polarized light in response to the plurality of magnetic subsidiary levels being the cooling lower level in the ground state of an atom, which is an object to be laser-cooled.
Sill further, an apparatus for laser cooling of atoms for laser-cooling atoms each involving a plurality of magnetic subsidiary levels as its cooling lower level being in a ground state in energy level according to the present invention comprises a plurality of coherent light sources outputting respectively a coherent light of a predetermined wavelength involving respectively a plurality of different polarized light in response to the plurality of magnetic subsidiary levels being the cooling lower level in the ground state of an atom, which is an object to be cooled; each coherent light of the predetermined wavelength containing the plurality of different polarized light output from the plurality of coherent light sources being sequentially emitted to the atom while keeping a predetermined time interval; and the polarized light of the coherent light emitted from the plurality of coherent light sources corresponding respectively to the plurality of different polarized light in response to the plurality of magnetic subsidiary levels being the cooling lower level in the ground state of the atom, which is the object to be laser-cooled.
The apparatus for laser cooling of atoms described in the above invention wherein at least one of the plurality of coherent light sources is that outputs selectively coherent light involving two different polarized light.
Further, the apparatus for laser cooling of atoms described in the above invention wherein the predetermined time interval is that substantially twice longer than spontaneous emission lifetime of the atom corresponding to a time required for absorptionxe2x80x94emission of one photon.
In addition, a coherent light source used for laser cooling of atoms according to the present invention comprises a mode-locked (lock) picosecond laser for outputting coherent light of a predetermined wavelength; a wavelength conversion element for converting a wavelength of the coherent light of the predetermined wavelength output from the mode-locked (lock) picosecond laser; a wavelength dispersion element for selecting coherent light of a desired wavelength from the coherent light, which has been subjected to wavelength conversion by means of the wavelength conversion element, to output the coherent light selected; and a feedback circuit for measuring a wavelength of the coherent light output from the wavelength dispersion element to output a signal to the mode-locked (lock) picosecond laser in such that the mode-locked (lock) picosecond laser outputs coherent light of a predetermined wavelength on the basis of the measured result.
Yet further, an apparatus for laser cooling of atoms for laser-cooling atoms each involving a plurality of magnetic subsidiary levels as its cooling lower level being in a ground state in energy level according to the present invention comprises a coherent light source producing coherent light of predetermined wavelength; a polarized light control means including a half-wavelength plate and an acousto-optic device, and controlling polarized light obtained from the coherent light output from the coherent light source by means of the half-wavelength plate to emit coherent light involving different polarized light to the atoms with a predetermined time interval; and chirped cooling being effected by changing time-varyingly a frequency by the use of the acousto-optic device to decelerate the atoms as well as to separate time-varyingly the polarized light obtained by means of the half-wavelength plate with the use of the acousto-optic device, besides to optimize the frequency thereby cooling the atoms by means of scattering force.
Furthermore, a coherent light source used for laser cooling of atoms according to the present invention comprises a first laser beam producing system for producing laser beam of a first wavelength; and a second laser beam producing system for producing laser beam of a second wavelength as well as for introducing the laser beam of the first wavelength produced in the first laser beam producing system thereinto to produce laser beam of a third wavelength as a result of sum frequency mixing of the laser beam of the first wavelength and the laser beam of the second wavelength.
Moreover, an apparatus for laser cooling of atoms for laser-cooling atoms each involving a plurality of magnetic subsidiary levels as its cooling lower level being in a ground state in energy level according to the present invention comprises a coherent light source including a first laser beam producing system for producing laser beam of a first wavelength, and a second laser beam producing system for producing laser beam of a second wavelength as well as for introducing the laser beam of the first wavelength produced in the first laser beam producing system thereinto to produce laser beam of a third wavelength as a result of sum frequency mixing of the laser beam of the first wavelength and the laser beam of the second wavelength; a polarized light control means including a half-wavelength plate and an acousto-optic device, and controlling polarized light obtained from the coherent light output from the coherent light source by means of the half-wavelength plate to emit coherent light involving different polarized light to the atoms with a predetermined time interval; and chirped cooling being effected by changing time-varyingly a frequency by the use of the acousto-optic device to decelerate the atoms as well as to separate time-varyingly the polarized light obtained by means of the half-wavelength plate with the use of the acousto-optic device, besides to optimize the frequency thereby cooling the atoms by means of scattering force.